1 Transects

Plant	Flowers	Date	lon	lat	ele	Month	Year	julian
Glossoloma oblongicalyx	4	2015-10-19	-78.59093	0.130838	2270	October	2015	292
Gasteranthus quitensis	2	2016-10-17	-78.59770	0.120070	1940	October	2016	291
Kohleria affinis	1	2016-12-13	-78.59534	0.126746	2110	December	2016	348
Columnea ciliata	3	2014-02-27	-78.59934	0.116682	1960	February	2014	58
Columnea medicinalis	1	2014-04-23	-78.59372	0.128700	2130	April	2014	113
Drymonia teuscheri	3	2016-07-28	-78.59245	0.129393	2200	July	2016	210

2 Interactions

3 Phylogeny

4 Traits

Plant	Flowers	Date	lon	lat	ele	Month	Year	julian
Glossoloma oblongicalyx	4	2015-10-19	-78.59093	0.130838	2270	October	2015	292
Gasteranthus quitensis	2	2016-10-17	-78.59770	0.120070	1940	October	2016	291
Kohleria affinis	1	2016-12-13	-78.59534	0.126746	2110	December	2016	348
Columnea ciliata	3	2014-02-27	-78.59934	0.116682	1960	February	2014	58
Columnea medicinalis	1	2014-04-23	-78.59372	0.128700	2130	April	2014	113
Drymonia teuscheri	3	2016-07-28	-78.59245	0.129393	2200	July	2016	210

4.0.1 Total Flowers

4.1 Peak date

As range

4.2 Infer absences

4.3 Species elevation ranges

4.4 Flowering Data Matrix

5 Baseline model

Equal probability of flowering at anytime.

## sink("model/threshold_baseline.jags")
## cat("
##     model {
##     
##     for (x in 1:Nobs){
## 
##     #Observation of a flowering plant
##     Y[x] ~ dbern(p[x])
##     logit(p[x]) <- alpha[Plant[x]] 
##     
##     #Residuals
##     discrepancy[x] <- abs(Y[x] - p[x])
##     
##     #Assess Model Fit
##     Ynew[x] ~ dbern(p[x])
##     discrepancy.new[x]<-abs(Ynew[x] - p[x])
##     }
##     
##     
##     #Sum discrepancy
##     fit<-sum(discrepancy)/Nobs
##     fitnew<-sum(discrepancy.new)/Nobs
##     
##     #Prediction
##     
##     for(x in 1:Npreds){
##     #predict value
##     
##     #Observation - probability of flowering
##     prediction[x] ~ dbern(p_new[x])
##     logit(p_new[x])<-alpha[PredPlant[x]]
##     
##     #predictive error
##     pred_error[x] <- abs(Ypred[x] - prediction[x])
##     }
##     
##     
##     #Predictive Error
##     fitpred<-sum(pred_error)/Npreds
##     
##     #Priors
##     
##     #Species level priors
##     
##     for (j in 1:Plants){
##     
##     #Intercept
##     #Intercept flowering count
##     alpha[j] ~ dnorm(0,0.386)
##     
##     } 
## 
##     }
##     ",fill=TRUE)
## 
## sink()

## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 2324
##    Unobserved stochastic nodes: 2926
##    Total graph size: 14658
## 
## Initializing model

6 Get Chains

6.0.1 Evaluate convergence

6.0.2 Posterior estimates

7 Phylogeny

7.1 Attraction

## sink("model/threshold_attraction.jags")
## cat("
##     model {
##     
##     for (x in 1:Nobs){
##     
##     #Observation of a flowering plant
##     Y[x] ~ dbern(p[x])
##     logit(p[x]) <- e[Plant[x],Month[x]]
##     
##     #Residuals
##     discrepancy[x] <- abs(Y[x] - p[x])
##     
##     #Assess Model Fit
##     Ynew[x] ~ dbern(p[x])
##     discrepancy.new[x]<-abs(Ynew[x] - p[x])
##     }
##     
##     #Sum discrepancy
##     fit<-sum(discrepancy)/Nobs
##     fitnew<-sum(discrepancy.new)/Nobs
##     
##     #Prediction
##     
##     for(x in 1:Npreds){
##     #predict value
##     
##     #Observation - probability of flowering
##     prediction[x] ~ dbern(p_new[x])
##     logit(p_new[x])<- e[NewPlant[x],NewMonth[x]]
##     
##     #predictive error
##     pred_error[x] <- abs(Ypred[x] - prediction[x])
##     }
##     
##     #Predictive Error
##     fitpred<-sum(pred_error)/Npreds
##     
##     #########################
##     #autocorrelation in error
##     #########################
##     
##     #For each of observation
##     for(y in 1:Months){
##     e[1:Plants,y] ~ dmnorm(zeros,tauC[,])
##     }
##     
##     ##covariance among similiar species
##     for(i in 1:Plants){
##     for(j in 1:Plants){
##     C[i,j] = exp(-lambda_cov * D[i,j])
##     }
##     }
##     
##     ## Covert variance to precision for each parameter, allow omega to shrink to identity matrix
##     vCov = omega*C[,] + (1-omega) * I
##     tauC=inverse(vCov*gamma)
##     
##     #Priors
##     
##     #Autocorrelation priors
##     gamma  = 10
##     
##     #Strength of covariance decay
##     lambda_cov = 5
##     omega = 1
##     }
##     ",fill=TRUE)
## 
## sink()
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 2324
##    Unobserved stochastic nodes: 2924
##    Total graph size: 18874
## 
## Initializing model

8 Get Chains

8.0.1 Evaluate convergence

8.0.2 Posterior estimates

Mean phylogenetic covariance

8.1 Decay in phylogenetic attraction

8.2 Repulsion

## sink("model/threshold_repulsion.jags")
## cat("
##     model {
##     
##     for (x in 1:Nobs){
##     
##     #Observation of a flowering plant
##     Y[x] ~ dbern(p[x])
##     logit(p[x]) <-  e[Plant[x],Month[x]]
##     
##     #Residuals
##     discrepancy[x] <- abs(Y[x] - p[x])
##     
##     #Assess Model Fit
##     Ynew[x] ~ dbern(p[x])
##     discrepancy.new[x]<-abs(Ynew[x] - p[x])
##     }
##     
##     
##     #Sum discrepancy
##     fit<-sum(discrepancy)/Nobs
##     fitnew<-sum(discrepancy.new)/Nobs
##     
##     #Prediction
##     
##     for(x in 1:Npreds){
##     #predict value
##     
##     #Observation - probability of flowering
##     prediction[x] ~ dbern(p_new[x])
##     logit(p_new[x])<- e[NewPlant[x],NewMonth[x]]
##     
##     #predictive error
##     pred_error[x] <- abs(Ypred[x] - prediction[x])
##     }
##     
##     #Predictive Error
##     fitpred<-sum(pred_error)/Npreds
##     
##     #########################
##     #autocorrelation in error
##     #########################
##     
##     #For each of observation
##     for(y in 1:Months){
##     e[1:Plants,y] ~ dmnorm(zeros,tauC[,])
##     }
##     
##     ##covariance among similiar species
##     for(i in 1:Plants){
##     for(j in 1:Plants){
##     C[i,j] = exp(-lambda_cov * D[i,j])
##     }
##     }
##     
##     ## Covert variance to precision for each parameter, allow omega to shrink to identity matrix
##     vCov = omega*C[,] + (1-omega) * I
##     tauC=vCov*gamma
##     
##     #Priors
##     
##     #Autocorrelation priors
##     gamma = 1
##     
##     #Strength of covariance decay
##     lambda_cov = 5
##     omega = 1
##     }
##     ",fill=TRUE)
## 
## sink()
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 2324
##    Unobserved stochastic nodes: 2924
##    Total graph size: 18872
## 
## Initializing model

9 Get Chains

9.0.1 Evaluate convergence

9.0.2 Posterior estimates

Mean phylogenetic covariance martix

9.1 Decay in phylogenetic repulsion

10 Traits

10.1 Trait Attraction

## sink("model/threshold_attraction.jags")
## cat("
##     model {
##     
##     for (x in 1:Nobs){
##     
##     #Observation of a flowering plant
##     Y[x] ~ dbern(p[x])
##     logit(p[x]) <- e[Plant[x],Month[x]]
##     
##     #Residuals
##     discrepancy[x] <- abs(Y[x] - p[x])
##     
##     #Assess Model Fit
##     Ynew[x] ~ dbern(p[x])
##     discrepancy.new[x]<-abs(Ynew[x] - p[x])
##     }
##     
##     #Sum discrepancy
##     fit<-sum(discrepancy)/Nobs
##     fitnew<-sum(discrepancy.new)/Nobs
##     
##     #Prediction
##     
##     for(x in 1:Npreds){
##     #predict value
##     
##     #Observation - probability of flowering
##     prediction[x] ~ dbern(p_new[x])
##     logit(p_new[x])<- e[NewPlant[x],NewMonth[x]]
##     
##     #predictive error
##     pred_error[x] <- abs(Ypred[x] - prediction[x])
##     }
##     
##     #Predictive Error
##     fitpred<-sum(pred_error)/Npreds
##     
##     #########################
##     #autocorrelation in error
##     #########################
##     
##     #For each of observation
##     for(y in 1:Months){
##     e[1:Plants,y] ~ dmnorm(zeros,tauC[,])
##     }
##     
##     ##covariance among similiar species
##     for(i in 1:Plants){
##     for(j in 1:Plants){
##     C[i,j] = exp(-lambda_cov * D[i,j])
##     }
##     }
##     
##     ## Covert variance to precision for each parameter, allow omega to shrink to identity matrix
##     vCov = omega*C[,] + (1-omega) * I
##     tauC=inverse(vCov*gamma)
##     
##     #Priors
##     
##     #Autocorrelation priors
##     gamma  = 10
##     
##     #Strength of covariance decay
##     lambda_cov = 5
##     omega = 1
##     }
##     ",fill=TRUE)
## 
## sink()
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 2324
##    Unobserved stochastic nodes: 2924
##    Total graph size: 19030
## 
## Initializing model

11 Get Chains

11.0.1 Evaluate convergence

11.0.2 Posterior estimates

11.1 Decay in trait attraction

11.2 Repulsion

## sink("model/threshold_repulsion.jags")
## cat("
##     model {
##     
##     for (x in 1:Nobs){
##     
##     #Observation of a flowering plant
##     Y[x] ~ dbern(p[x])
##     logit(p[x]) <-  e[Plant[x],Month[x]]
##     
##     #Residuals
##     discrepancy[x] <- abs(Y[x] - p[x])
##     
##     #Assess Model Fit
##     Ynew[x] ~ dbern(p[x])
##     discrepancy.new[x]<-abs(Ynew[x] - p[x])
##     }
##     
##     
##     #Sum discrepancy
##     fit<-sum(discrepancy)/Nobs
##     fitnew<-sum(discrepancy.new)/Nobs
##     
##     #Prediction
##     
##     for(x in 1:Npreds){
##     #predict value
##     
##     #Observation - probability of flowering
##     prediction[x] ~ dbern(p_new[x])
##     logit(p_new[x])<- e[NewPlant[x],NewMonth[x]]
##     
##     #predictive error
##     pred_error[x] <- abs(Ypred[x] - prediction[x])
##     }
##     
##     #Predictive Error
##     fitpred<-sum(pred_error)/Npreds
##     
##     #########################
##     #autocorrelation in error
##     #########################
##     
##     #For each of observation
##     for(y in 1:Months){
##     e[1:Plants,y] ~ dmnorm(zeros,tauC[,])
##     }
##     
##     ##covariance among similiar species
##     for(i in 1:Plants){
##     for(j in 1:Plants){
##     C[i,j] = exp(-lambda_cov * D[i,j])
##     }
##     }
##     
##     ## Covert variance to precision for each parameter, allow omega to shrink to identity matrix
##     vCov = omega*C[,] + (1-omega) * I
##     tauC=vCov*gamma
##     
##     #Priors
##     
##     #Autocorrelation priors
##     gamma = 1
##     
##     #Strength of covariance decay
##     lambda_cov = 5
##     omega = 1
##     }
##     ",fill=TRUE)
## 
## sink()
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 2324
##    Unobserved stochastic nodes: 2924
##    Total graph size: 19028
## 
## Initializing model

12 Get Chains

12.0.1 Evaluate convergence

12.0.2 Posterior estimates

12.1 Decay in trait repulsion

13 Interaction

13.1 Attraction

## sink("model/threshold_attraction.jags")
## cat("
##     model {
##     
##     for (x in 1:Nobs){
##     
##     #Observation of a flowering plant
##     Y[x] ~ dbern(p[x])
##     logit(p[x]) <- e[Plant[x],Month[x]]
##     
##     #Residuals
##     discrepancy[x] <- abs(Y[x] - p[x])
##     
##     #Assess Model Fit
##     Ynew[x] ~ dbern(p[x])
##     discrepancy.new[x]<-abs(Ynew[x] - p[x])
##     }
##     
##     #Sum discrepancy
##     fit<-sum(discrepancy)/Nobs
##     fitnew<-sum(discrepancy.new)/Nobs
##     
##     #Prediction
##     
##     for(x in 1:Npreds){
##     #predict value
##     
##     #Observation - probability of flowering
##     prediction[x] ~ dbern(p_new[x])
##     logit(p_new[x])<- e[NewPlant[x],NewMonth[x]]
##     
##     #predictive error
##     pred_error[x] <- abs(Ypred[x] - prediction[x])
##     }
##     
##     #Predictive Error
##     fitpred<-sum(pred_error)/Npreds
##     
##     #########################
##     #autocorrelation in error
##     #########################
##     
##     #For each of observation
##     for(y in 1:Months){
##     e[1:Plants,y] ~ dmnorm(zeros,tauC[,])
##     }
##     
##     ##covariance among similiar species
##     for(i in 1:Plants){
##     for(j in 1:Plants){
##     C[i,j] = exp(-lambda_cov * D[i,j])
##     }
##     }
##     
##     ## Covert variance to precision for each parameter, allow omega to shrink to identity matrix
##     vCov = omega*C[,] + (1-omega) * I
##     tauC=inverse(vCov*gamma)
##     
##     #Priors
##     
##     #Autocorrelation priors
##     gamma  = 10
##     
##     #Strength of covariance decay
##     lambda_cov = 5
##     omega = 1
##     }
##     ",fill=TRUE)
## 
## sink()
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 2324
##    Unobserved stochastic nodes: 2924
##    Total graph size: 19030
## 
## Initializing model

13.1.1 Evaluate convergence

13.1.2 Posterior estimates

Mean interaction covariance

13.2 Decay in interaction attraction

13.3 Repulsion

## sink("model/threshold_repulsion.jags")
## cat("
##     model {
##     
##     for (x in 1:Nobs){
##     
##     #Observation of a flowering plant
##     Y[x] ~ dbern(p[x])
##     logit(p[x]) <-  e[Plant[x],Month[x]]
##     
##     #Residuals
##     discrepancy[x] <- abs(Y[x] - p[x])
##     
##     #Assess Model Fit
##     Ynew[x] ~ dbern(p[x])
##     discrepancy.new[x]<-abs(Ynew[x] - p[x])
##     }
##     
##     
##     #Sum discrepancy
##     fit<-sum(discrepancy)/Nobs
##     fitnew<-sum(discrepancy.new)/Nobs
##     
##     #Prediction
##     
##     for(x in 1:Npreds){
##     #predict value
##     
##     #Observation - probability of flowering
##     prediction[x] ~ dbern(p_new[x])
##     logit(p_new[x])<- e[NewPlant[x],NewMonth[x]]
##     
##     #predictive error
##     pred_error[x] <- abs(Ypred[x] - prediction[x])
##     }
##     
##     #Predictive Error
##     fitpred<-sum(pred_error)/Npreds
##     
##     #########################
##     #autocorrelation in error
##     #########################
##     
##     #For each of observation
##     for(y in 1:Months){
##     e[1:Plants,y] ~ dmnorm(zeros,tauC[,])
##     }
##     
##     ##covariance among similiar species
##     for(i in 1:Plants){
##     for(j in 1:Plants){
##     C[i,j] = exp(-lambda_cov * D[i,j])
##     }
##     }
##     
##     ## Covert variance to precision for each parameter, allow omega to shrink to identity matrix
##     vCov = omega*C[,] + (1-omega) * I
##     tauC=vCov*gamma
##     
##     #Priors
##     
##     #Autocorrelation priors
##     gamma = 1
##     
##     #Strength of covariance decay
##     lambda_cov = 5
##     omega = 1
##     }
##     ",fill=TRUE)
## 
## sink()
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 2324
##    Unobserved stochastic nodes: 2924
##    Total graph size: 19028
## 
## Initializing model

14 Get Chains

14.0.1 Evaluate convergence

14.0.2 Posterior estimates

Mean interaction covariance martix

14.1 Decay in interaction repulsion

15 Model Comparison

15.1 E: The effect of autocorrelation on mean flowering occurrence

15.1.1 E: The effect of autocorrelation

Dig into one example.

Glossoloma purpureum

16 By site

16.1 1300m - 1500m

16.2 1500-1700m

16.3 1700-1900

16.4 1900-2100m

16.5 2100-2300m

16.6 2300m - 2500m

16.7 Omega: The magnitude of the effect of autocorrelation on mean flowering occurrence

16.8 Gamma: The variance of the effect of autocorrelation on mean flowering occurrence

16.9 Lambda: The decay in autocorrelation effect

16.10 Decay in autocorrelation effect

17 Model Fit

17.1 Bayesian pvalue

## # A tibble: 7 x 2
##   Model                       p
##   <chr>                   <dbl>
## 1 baseline                0.598
## 2 interaction_attraction  0.151
## 3 interaction_repulsion   1    
## 4 phylogenetic_attraction 0.114
## 5 phylogenetic_repulsion  1    
## 6 trait_attraction        0.107
## 7 trait_repulsion         1

Without baseline

## # A tibble: 6 x 2
##   Model                       p
##   <chr>                   <dbl>
## 1 interaction_attraction  0.151
## 2 interaction_repulsion   1    
## 3 phylogenetic_attraction 0.114
## 4 phylogenetic_repulsion  1    
## 5 trait_attraction        0.107
## 6 trait_repulsion         1

17.2 Overall

Model	mean	lower	upper
trait_repulsion	0.3571308	0.3493401	0.3644422
phylogenetic_repulsion	0.3433308	0.3354418	0.3510792
interaction_repulsion	0.3224660	0.3141719	0.3307715
interaction_attraction	0.2269077	0.2198348	0.2334874
phylogenetic_attraction	0.2256049	0.2187191	0.2324988
trait_attraction	0.2249972	0.2183616	0.2318602

17.2.1 Without baseline

17.3 By Species